On a GSX the gas tank is directly under the handlebars, I don't know where you would cut an access hole to get to the fuel baffle.
I've found that at least 9 out of 10 times the cause is the float in the fuel baffle, just replace the float in the fuel baffle with the newer molded type, not so easy on the GSX. You will need to remove the gas, remove the rubber straps on the fuel tank and oil tank. Loosen the steering and use a block of wood to hold it up. Slide the fuel tank forward and remove the baffle through the front access.
Since you've done all this work check the fuse with an ohm meter to make sure it's not the fuse.
Lou